1. Statement of the Technical Field
The inventive arrangements relate generally to transmission line stubs, and more particularly for transmission line stubs that can be dynamically tuned.
2. Description of the Related Art
Transmission line stubs are commonly used in radio frequency (RF) circuits. A transmission line stub is sometimes said to be resonant at a particular frequency, meaning the line has impedance characteristics similar to a resonant circuit at that frequency. Accordingly, transmission line stubs are often referred to as resonant lines or tuned lines. It should be noted, however, that transmission line stub impedance characteristics are actually a function of voltage reflections, not circuit resonance. On printed circuit boards or substrates, transmission line stubs are typically implemented by creating a line with at least one port at the input, and either an open-circuit or short-circuit to ground at the termination. The input impedance to an open or shorted transmission line stub is typically resistive when the length of the transmission line stub is an even or odd multiple of a quarter-wavelength of the operational frequency. That is, the input to the transmission line stub is at a position of voltage maxima or minima. When the input to the transmission line stub is at a position between the voltage maxima and minima points, the input impedance can have reactive components. Consequently, properly chosen transmission line stubs may be used as parallel-resonant, series-resonant, inductive, or capacitive circuits.
In some instances, a transmission line stub can be capacitively coupled to ground at the termination. When a transmission line stub is terminated in capacitance, the capacitor does not permanently absorb energy, but returns all of the energy to the circuit. Current and voltage are in phase when they arrive at the end of the line. But in flowing through the series combination of the capacitor and the characteristic impedance (ZO) of the transmission line stub, the phase relationship of current and voltage is changed, resulting in a standing wave. The standing wave voltage is minimum at a distance of exactly ⅛ wavelength from the end if the termination when the termination capacitance has the same impedance magnitude is equal to ZO. If the magnitude of the capacitive impedance is greater than ZO (smaller capacitance value), the termination looks more like an open circuit and the voltage minimum moves away from the end. If the magnitude of the capacitive impedance is smaller than ZO, the voltage minimum moves closer to the end. As the voltage minimums and maximums move along the transmission line stubs, so do the regions on the transmission line stub where the transmission line stub acts as an inductance or a capacitance.
Transmission line stubs in RF circuits are typically formed in one of three ways. One configuration known as microstrip, places the signal line on the top of a board surface. A second conductive layer, commonly referred to as a ground plane, is spaced apart from and below the signal line. A second type of configuration known as—buried microstrip is similar except that the signal line is covered with a dielectric substrate material. In a third configuration known as stripline, the signal line is sandwiched between two electrically conductive (ground) planes. Other configurations, including waveguide stubs, are also known in the art.
Low permittivity printed circuit board materials are ordinarily selected for implementing RF circuit designs, including transmission line stubs. For example, polytetrafluoroethylene (PTFE) based composites such as RT/duroid® 6002 (permittivity of 2.94; loss tangent of 0.009) and RT/duroid® 5880 (permittivity of 2.2; loss tangent of 0.0007), both available from Rogers Microwave Products, Advanced Circuit Materials Division, 100 S. Roosevelt Ave, Chandler, Ariz. 85226, are common board material choices.
Two important characteristics of dielectric materials are permittivity (sometimes called the relative permittivity or εr) and permeability (sometimes referred to as relative permeability or μr). The relative permittivity and permeability determine the propagation velocity of a signal, which is approximately inversely proportional to √{square root over (με)}. The propagation velocity directly affects the electrical length of a transmission line and therefore the physical length of a transmission line stub.
Further, ignoring loss, the characteristic impedance of a transmission line, such as stripline or microstrip, is equal to √{square root over (L1/C1)} where L1 is the inductance per unit length and C1 is the capacitance per unit length. The values of L1 and C1 are generally determined by the permittivity and the permeability of the dielectric material(s) used to separate the transmission line structures as well as the physical geometry and spacing of the line structures. Accordingly, the overall geometry of a transmission line stub will be highly dependent on the permittivity and permeability of the dielectric substrate.
The electrical characteristics of transmission line stubs generally cannot be modified once formed on an RF circuit board. This is not a problem where only a fixed frequency response is needed. The geometry of the transmission line can be readily designed and fabricated to achieve the proper characteristic impedance. When a variable frequency response is needed, however, use of a fixed length transmission line stub can be a problem.
A similar problem is encountered in RF circuit design with regard to optimization of circuit components for operation on different RF frequency bands. Line impedances and lengths that are optimized for a first RF frequency band may provide inferior performance when used for other bands, either due to impedance variations and/or variation in electrical length. Such limitations can limit the effective operational frequency range for a given RF system.